Question

If power = 150 kW, torque = 100 Nm, find the angular velocity \(\omega\).

Hint:

To find angular velocity, use the formula \( P = \tau \cdot \omega \), where \( P \) is the power, \( \tau \) is the torque, and \( \omega \) is the angular velocity.

Answer 1

Step 1: Use the formula relating power and torque.
The power \( P \) in rotational motion is related to torque \( \tau \) and angular velocity \( \omega \) by the formula: \[ P = \tau \cdot \omega \]
Step 2: Rearrange the equation to solve for angular velocity.
Rearrange the equation to solve for \( \omega \): \[ \omega = \frac{P}{\tau} \]
Step 3: Substitute the known values.
Substitute \( P = 150 \, \text{kW} = 150 \times 10^3 \, \text{W} \) and \( \tau = 100 \, \text{Nm} \): \[ \omega = \frac{150 \times 10^3}{100} = 1500 \, \text{rad/s} \] Thus, the angular velocity is: \[ \boxed{1500 \, \text{rad/s}} \]